Resonances for a semi-classical Schrödinger operator near a non trapping energy level
type: Item
instance of: scholarly article
title: Resonances for a semi-classical Schrödinger operator near a non trapping energy level
zbMATH Open document ID: 0947.34070
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 2000-11-02T00:00:00Z
review text: Summary: The author gives an example of a short range potential \(V\) on the real line that is dilation analytic at infinity, non trapping at energy \(E>0\), but oscillating in the neighborhood of some points, so rapidly that the Schrödinger operator \(P=-h^2 \Delta+V\) shows a string of resonances near \(E\) in the lower half plane when \(h>0\) is small enough. The extended states behave as standing waves partially reflected off the bumps of \(V\). Such a potential is the analogue of the Wigner-Von Neumann potential in the case of embedded eigenvalues.
Mathematics Subject Classification ID: 34L40
Mathematics Subject Classification ID: 81Q20
zbMATH DE Number: 1439796
zbMATH Keywords: resonances
zbMATH Keywords: semi-classical Schrödinger operator
zbMATH Keywords: short range potential
zbMATH Keywords: bumps
zbMATH Keywords: Wigner-Von Neumann potential
zbMATH Keywords: embedded eigenvalues
author: Michel Rouleux
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195144421
OpenAlex ID: W2037019768
cites work: Scattering frequencies and Gevrey 3 singularities
cites work: On the location of resonances for Schrödinger operators in the semiclassical limit. I: Resonances free domains
cites work: The shape resonance
cites work: Q4040478
cites work: Semiclassical resonances generated by a closed trajectory of hyperbolic type
cites work: Q4139272
cites work: Semiclassical theory of shape resonances in quantum mechanics
cites work: Q3756006
cites work: Multiple resonances in the semi-classical limit
cites work: Asymptotic behavior of Jost functions near resonance points for Wigner–von Neumann type potentials
cites work: Zero-range potentials with internal structures and the inverse scattering problem
cites work: Propagation des singularites Gevrey pourla diffraction
cites work: Q3996331
cites work: Q3739534
cites work: Singularities and energy decay in acoustical scattering
cites work: Q4004053
cites work: Perturbation of resonances
cites work: Q4185363
cites work: Complex Scaling and the Distribution of Scattering Poles
DOI: 10.2977/PRIMS/1195144421
description: scientific article; zbMATH DE number 1439796